Dr. Richard Kim Profile

Dr. Richard Kim

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Proceedings Article | 22 April 2020 Presentation + Paper

Stochastic inventory control modelling for large satellite constellations

Richard Kim

Proceedings Volume 11422, 114220G (2020) https://doi.org/10.1117/12.2557397

KEYWORDS: Satellites, Failure analysis, Global Positioning System, Stochastic processes, Systems modeling, Process modeling, Surveillance, Space operations, Space sensors

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As space technologies mature, the cost of inserting materiel into orbit continues to decrease. Advances in the miniaturization of hardware and decreasing launch costs have resulted in space becoming increasingly accessible to nations and organizations. This is especially the case with the low Earth orbit, which is used as a staging environment for satellite constellations that provide imaging, communications, and other services. While very large satellite constellations were previously fielded by only a handful of nations, with increasing ease of access to space, many more space-faring organizations are designing systems of hundreds or thousands of satellites. This has led to the emergence of a new problem: how to manage satellite inventories in an optimal manner. To address this challenge, we propose the use of Markov decision process (MDP) models to compute the optimal fielding policy for satellites within a constellation, given the current state. We apply this model to the Global Positioning System (GPS), a system which requires a minimum of 24 satellites to provide system-level operations, but which consists of approximately 30 satellites in medium Earth orbit. Our analysis, performed entirely independently from the GPS sustainment rationale, suggests that the mathematically optimal steady-state inventory level for the GPS constellation is 31 satellites, which provides affirmation for both the GPS sustainment policy and our proposed model. In addition, we perform sensitivity analysis on various parameters such as the risk aversion of the decision makers and ordering limits of additional satellites.

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